Power converters are used to convert one form of energy to another (e.g., AC to AC, AC to DC, DC to AC, and DC to DC) thereby making it usable to the end equipment, such as computers, automobiles, electronics, telecommunications, space systems and satellites, and motors. Every application of power electronics involves some aspect of control. Converters are typically identified by their capability and/or configurations, such as, buck converters, boost converters, buck-boost converters, boost-buck converters (Ćuk), etc. For example, DC-DC converters belong to a family of converters known as “switching converters” or “switching regulators.” This family of converters is the most efficient because the conversion elements switch from one state to another, rather than needlessly dissipating power during the conversion process. Essentially there is a circuit with switches and two configurations (each can be modeled as linear systems) in which the converter resides according to the switch positions. The duty ratio (d) is the ratio indicating the time in which a chosen switch is in the “on” position while the other switch is in the “off” position, and this d is considered to be the control input. Input d is usually driven by pulse-width-modulation (“PWM”) techniques.
Switching from one state to another and the accompanying nonlinearity of the system causes problems. State space averaging reduces the switching problems to make the system, in general, a nonlinear averaged system for a boost converter or a buck-boost converter. But, control of the system under these nonlinear effects becomes difficult when certain performance objectives must be met. Linearization is mostly accomplished through a Taylor series expansion. Nonlinear terms of higher orders are thrown away and a linear approximation replaces the nonlinear system. This linearization method has proven effective for stabilizing control loops at a specific operating point. However, use of this method requires making several assumptions, one of them being so-called “small signal operation.” This works well for asymptotic stability in the neighborhood of the operating point, but ignores large signal effects which can result in nonlinear operation of the control loop when, for example, an amplifier saturates during startup, or during transient modes, such as load or input voltage changes. Once nonlinear operation sets in, the control loop can have equilibrium points unaccounted for in the linearization.
One of the most widely used methods of pulse-width modulation is trailing-edge modulation (“TEM”), wherein the on-time pulse begins on the clock and terminates in accordance with a control law. Unstable zero dynamics associated with TEM with switch on-time sampling in the continuous conduction mode (“CCM”) prevent the use of an input-output feedback linearization because it would result in an unstable operating point for boost and buck-boost converters. The other control method is LEM, wherein the on-time pulse begins in accordance with a control law and terminates on the clock. The difference between LEM and TEM is that in TEM the pulse-width is determined by the instantaneous control voltage vc prior to switch turn-off, whereas in LEM the pulse-width is determined by vc prior to switch turn-on.
Further, it is well known in the art that pulse-width modulation (“PWM”) boost and buck-boost power converters exhibit right half plane zero effects when trailing edge modulation with on time switch sampling is employed. This makes control design extremely difficult. It has been shown that if leading edge modulation with off time switch sampling is used with a sufficiently large equivalent series resistance (“ESR”) Rc of the output capacitor, then left half plane zero effects emerge. This enables much easier control design.
Therefore, there is a need for a system and method for controlling ripple of DC-DC converters with LEM control to alleviate dependence on the value of Rc under LEM in either analog or digital converter systems while delivering left plane zero effects.